Osmosis is the phenomenon of the movement of Solvent molecules from lower solute concentration to higher solute concentration through a semi-permeable membrane to make solute concentration equal on both sides.
Osmosis is diffusion of water across a semi-permeable membrane. Salt is too big to pass through a cell membrane, but water molecules can fit. Since everything wants to reach equilibrium, the only thing that can flow to create equal concentrations is water. Eg. Saline drips at the hospital - same ratio of salt water as is in your cells.
Diffusion is movement of solute molecules from higher concentration to lower concentration of solvent with in the solvent. Eg. Perfume through air